1. Filed of the Invention
The present invention relates to a method of determining the amplitudes and phases to be applied to the various channels of an electromagnetic signal transmission network.
2. Background of the Invention
It is advantageously applicable in determining the amplitudes and phases to be applied to the various channels of a telecommunications satellite antenna.
Conventionally, these amplitudes and phases are calculated by implementing inverse Fourier transform processes.
The free-space radiation pattern at infinity is obtained to a first approximation by applying the field Fourier transform to the aperture of the antenna. For a given direction, the field can thus be obtained to the first order by the inverse Fourier transform of a pattern which concentrates the energy transmitted in said direction. The result is a complex vector which gives the amplitudes and phases at the various sources of the array antenna.
Implementing a complete network requires the same calculation to be performed for different directions.
Such processing is simple to implement when the various sources and directions occupy a regular square or rectangular grid since two-dimensional fast Fourier transform (FFT) algorithms can be applied easily.
It is more difficult to perform when the various sources are on a regular triangular grid giving hexagonal cells. Nevertheless, this configuration is the more advantageous, in particular for the antennas of telecommunications satellites for use with mobile stations.
It is known that on the ground it is desirable to implement cells that are hexagonal, thus enabling better uniformity in the power received than with cells that are rectangular or square, and even that it is desirable to use circular or hexagonal elements for the transmission network since they enable the plane to be tiled with amplitude that is more uniform. The overall shape of the antenna must itself approximate to a circle or a hexagon.
An algorithm known as the hexagonal FFT is used for this purpose, which algorithm is derived from the rectangular FFT algorithm by eliminating every other point in a staggered configuration and by choosing a ratio of 3 between the height and the width of the unit pitches dy and dx of the rectangles.
An effect of this staggered sampling of the starting domain is to require the transformed domain to be tiled in a staggered configuration. Likewise, sampling the transformed domain in a staggered configuration requires the starting domain to be tiled in a staggered configuration.
Nevertheless, the solutions that have been proposed until now for tiling a triangular grid with hexagons are not entirely satisfactory.
As shown in FIG. 1, the solution that is generally used consists in shortening three sides of each hexagon. Hexagons with three short sides can be used to tile the triangular grid in a staggered configuration, with the staggered tiling being reducible to normal rectangular tiling by considering two hexagons, thus giving a total number of working points equal to 6n2.
For a description of that solution, reference can advantageously be made to the following publication:
xe2x80x9cThe processing of hexagonally sampled two-dimensional signalsxe2x80x9d by R. Mersereau, Proceedings of the IEEE, Vol. 67, No. 6, June 1979.
That type of sampling nevertheless suffers from the drawback of disturbing the uniformity and order 6 symmetry of the power distribution, particularly for hexagons of small size.
In particular, a hexagon of side of length n (n+1 points along a side) has N=3n(n+1)+1 points whereas a hexagon with three short sides has only 3n2 points, which for small values gives the following table:
The present invention proposes a method in which a triangular grid is tiled by means of complete hexagons.
Thus, the invention provides a method of determining the altitudes and phases to be applied to the various channels of an electromagnetic signal transmission network whose sources are disposed in a triangular grid, the method being characterized in that said grid is tiled with hexagons having six equal sides, the hexagon tiles implemented in this way being distributed over said grid in such a manner that two successive tiles in the height direction of the rectangular grid equivalent to said triangular grid are offset in the width direction by one unit pitch, in that a Fourier transform is applied to the resulting tiling, in that the directions corresponding to the transmission directions are selected on the resulting new grid (result of the transform), in that the inverse Fourier transform is implemented on those directions, and in that the amplitude and phase coefficients to be applied to the various channels of the transmission network are deduced from said inverse Fourier transform.